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Byju's Answer
Standard VIII
Mathematics
Dilations
In figure, ...
Question
In figure,
Δ
A
B
C
is an equilateral triangle. Points
f
,
D
and
E
are midpoints of side
A
B
, side
B
C
, side
A
C
respectively. Show that
Δ
F
E
D
is an equilateral triangle.
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Solution
E
F
|
|
B
C
By basic proportionality theorm ,
Δ
A
F
E
∼
Δ
A
B
C
Similarly ,
Δ
F
B
D
∼
Δ
A
B
C
Δ
E
C
D
∼
Δ
A
C
B
Att point
D
∠
B
D
F
+
∠
F
D
E
+
∠
E
D
C
=
180
60
+
∠
F
D
E
+
60
=
180
∠
F
D
E
=
60
∘
Similarly,
∠
D
E
F
=
∠
D
F
E
=
60
∘
Hence
Δ
D
E
F
is equilateral triangle.
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Q.
In the given figure,
∆
ABC is an equilateral traingle. Points F,D and E are midpoints of side AB, side BC, side AC respectively. Show that
∆
FED is an equilateral traingle.